This invention relates to a method and apparatus for determining the distribution of particle sizes of a scattering medium of unknown chemical composition. The medium may consist of a composite mixture of arbitrary numbers of chemically different particles embedded in various gases.
There is a continuing need to determine the size distribution of any arbitrary number of particle species which may present a distribution in their refractive indices, and which may be embedded in a scattering medium of unknown chemical composition, for such industrial purposes as environmental pollution monitoring and control, chemical analyses, aeronautical engineering and rocket engineering as well as for such other purposes as meteorological research, geophysical research, and biomedical analyses. The composite mixture of particles and gases may be contained in an experimental chamber, suspended freely in the air, or suspended in fluids such as medical plasmas, or in any other similar situation where particulate sizes must be determined without disturbing the sample.
Conventional direct sampling methods where particles are thermally precipitated, impacted or otherwise mechanically collected, as well as in situ imaging methods, present several problems. Some of these problems are: disturbing of sample, low sampling rate, discontinuous sampling, collection efficiency problems, long sampling time and painstaking analyses. Additionally, they cannot be used as remote sensors for realtime operation.
To avoid these problems of direct sampling, and at the same time provide a remote sensing capability, methods have been developed which exploit the forward light scattering properties of particles at frequencies within the range 0.198 to 4.070 inverse micrometers (.mu.m.sup.-1) or within any larger range extending down to 0.02 .mu.m.sup.1 and up to 9.27 .mu.m.sup.-1. Incident light, I.sub.o, possessing a spectrum of frequencies in the ranges above specified, is characterized ony by its wavenumber, .sigma..sub.i, the reciprocal of the wavelength, .lambda..sub.i. Its direction of propagation, .theta..sub.i, is the direction of reference, .theta..sub.i =0. The subscript, i, here stands for "incidence." Particles are characterized by their nature and micro-structure, respectively represented by a refractive index, m, a complex number, and a size distribution, n (r), representing a partial concentration per unit volume and per unit increment of the radius r. Only n (r) is independent of the wavenumber. The various particles, assumed to be spherical in shape, may also present a distribution in m itself. Gases will be similarly characterized by their number density, i.e. number of atoms or molecules per unit volume, refractive index and geometrical shape. Scattered light, on the other hand, is characterized by its wavenumber, .sigma..sub.s, and direction, .theta..sub.s, of propagation. Here the subscript, s, stands for "scattering." The direction, .theta..sub.s, is thus the scattering angle with reference to the incident light direction .theta..sub.i.
For a given incident light, i.e., for a situation where .sigma..sub.i and .theta..sub.i are given, and for a given assembly of scatterers, i.e., for an assembly of particles of given refractive indices, m(.nu..sub.s), and size distribution, n (r), Mie's theory of scattering by a conducting sphere enables us to determine the scattered light for any arbitrary .sigma..sub.s and .theta..sub.s. Conversely if the incident light is known for any .sigma..sub.i and .theta..sub.i to be prescribed, and the scattered light is measured for various .sigma..sub.s and .theta..sub.s to be also prescribed, we should be able in principle to infer the properties of the particles, that is their size distribution, and refractive index values at the various .sigma..sub.s. In other words, Mie's theory enables us to compute the output, I.sub.s, in all its detailed variations if we know the input, I.sub.o, and the properties of the particles m(.sigma..sub.s) and n(r). However, what is of interest is a determination of the scatterers from a knowledge of the input, I.sub.o, and the output, I.sub.s. But from an inversion of Mie's theory it would be possible to determine only the combined relation between the refractive indices, m(.sigma..sub.s), and size distribution, n(r), and not the size distribution separately.
It has been discovered that the Fraunhofer theory of angular diffraction of light of fixed single frequency at an aperture in a plane screen can be extended to a range of multiple frequencies. Under these conditions, the light scattered by a particle is essentially independent of the refractive index, m(.sigma..sub.s), and depends only on its size as though the particle were an aperture in a screen of the same radius. It has also been discovered that, working within the restricted domain of applicability of the theory thus extended (.theta..sub.s between 100 and 200 minutes of arc, approximately, preferably .theta..sub.s =150 minutes; and 0.2 .mu.m.sup.-1 .ltoreq..sigma..sub.s .ltoreq.4.0 .mu.m.sup.-1, approximately), it is possible to determine size distribution, n (r), independently of refractive indices m(.sigma..sub.s), i.e., to determine size distribution of particles of radius larger than approximately one micrometer (.mu.m) without knowing anything of their refractive indices, from known incident light, I.sub.o, and measured scattered light, I.sub.s.
If the assembly of scatterers under study consists of particles of j different species and k different gases, the identical determination of n (r) can still be made provided only j, k, and the so-called depolarization factor of each gas (this is defined as the ratio of scattered intensities in directions parallel and perpendicular to the plane of scattering for an incident beam of natural light), .rho..sub.k, are known.